Analysis of the band structure of transient in-plane elastic waves based on the localized radial basis function collocation method

In this paper, the localized radial basis function collocation method is applied to investigate the in-plane elastic wave propagation of 2D phononic crystals. The direct method with local support domain in one line is used to enhance the stability of the localized radial basis function collocation method when dealing with the derivative calculations in the boundary and interface conditions. The Houbolt method is employed to discretize the time, and then the Fast Fourier Transform is adopted to obtain the band structure according to the wave vectors in the first Brillouin Zone. Different acoustic impedance ratios, filling rates, and lattice forms are studied. The numerical results can be used to validate the band structures obtained directly from the frequency domain.